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Simplifying x2 + -14x = 155 Reorder the terms: -14x + x2 = 155 Solving -14x + x2 = 155 Solving for variable 'x'. Reorder the terms: -155 + -14x + x2 = 155 + -155 Combine like terms: 155 + -155 = 0 -155 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + -14x + 155 + x2 = 0 + 155 Reorder the terms: -155 + 155 + -14x + x2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + -14x + x2 = 0 + 155 -14x + x2 = 0 + 155 Combine like terms: 0 + 155 = 155 -14x + x2 = 155 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 155 + 49 Reorder the terms: 49 + -14x + x2 = 155 + 49 Combine like terms: 155 + 49 = 204 49 + -14x + x2 = 204 Factor a perfect square on the left side: (x + -7)(x + -7) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + -7) equal to 14.282856857 and -14.282856857.Subproblem 1
x + -7 = 14.282856857 Simplifying x + -7 = 14.282856857 Reorder the terms: -7 + x = 14.282856857 Solving -7 + x = 14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 14.282856857 + 7 Combine like terms: -7 + 7 = 0 0 + x = 14.282856857 + 7 x = 14.282856857 + 7 Combine like terms: 14.282856857 + 7 = 21.282856857 x = 21.282856857 Simplifying x = 21.282856857Subproblem 2
x + -7 = -14.282856857 Simplifying x + -7 = -14.282856857 Reorder the terms: -7 + x = -14.282856857 Solving -7 + x = -14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -14.282856857 + 7 Combine like terms: -7 + 7 = 0 0 + x = -14.282856857 + 7 x = -14.282856857 + 7 Combine like terms: -14.282856857 + 7 = -7.282856857 x = -7.282856857 Simplifying x = -7.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.282856857, -7.282856857}
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